On tame embeddings of solenoids into 3-space
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2006
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| _version_ | 1866910516232847360 |
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| author | Jiang, Boju Wang, Shicheng Zheng, Hao Zhou, Qing |
| author_facet | Jiang, Boju Wang, Shicheng Zheng, Hao Zhou, Qing |
| contents | Solenoids are ``inverse limits'' of the circle, and the classical knot theory is the theory of tame embeddings of the circle into the 3-space. We give some general study, including certain classification results, of tame embeddings of solenoids into the 3-space as the ``inverse limits'' of the tame embeddings of the circle.
Some applications are discussed. In particular, there are ``tamely'' embedded solenoids $Σ\subset \R^3$ which are strictly achiral. Since solenoids are non-planar, this contrasts sharply with the known fact that if there is a strictly achiral embedding $Y\subset \R^3$ of a compact polyhedron $Y$, then $Y$ must be planar. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_0611900 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | On tame embeddings of solenoids into 3-space Jiang, Boju Wang, Shicheng Zheng, Hao Zhou, Qing Geometric Topology Dynamical Systems 57N10, 37E99, 54C25 Solenoids are ``inverse limits'' of the circle, and the classical knot theory is the theory of tame embeddings of the circle into the 3-space. We give some general study, including certain classification results, of tame embeddings of solenoids into the 3-space as the ``inverse limits'' of the tame embeddings of the circle. Some applications are discussed. In particular, there are ``tamely'' embedded solenoids $Σ\subset \R^3$ which are strictly achiral. Since solenoids are non-planar, this contrasts sharply with the known fact that if there is a strictly achiral embedding $Y\subset \R^3$ of a compact polyhedron $Y$, then $Y$ must be planar. |
| title | On tame embeddings of solenoids into 3-space |
| topic | Geometric Topology Dynamical Systems 57N10, 37E99, 54C25 |
| url | https://arxiv.org/abs/math/0611900 |